Maria Fernanda Elbert

Stability of hypersurfaces with vanishing r-mean curvature in euclidean space

Hypersurfaces of euclidean spaces with vanishing r-mean curvature generalize minimal hypersurfaces (case r = I) and include the important case of scalar curvature (r = 2). They are critical points of variational problems and a notion of stability can be assigned to them. When their defining equations are elliptic, we obtain a criterion for stability of bounded domains of such hypersurfaces that generalizes a known theorem of Barbosa and do Carmo for stability of minimal surfaces.

On complete graphs with negative r-mean curvature

We generalize Efimov’s Theorem for graphs in Euclidean space using the scalar curvature, with an additional hypothesis on the second fundamental form.

Existence of vertical ends of mean curvature 1/2 in ℍ²×ℝ

We prove existence of graphs over exterior domains of H2 × {0}, of constant mean curvature H = 1 2 in H2 × R and weak growth equal to the embedded rotational examples.